Subgroups — D₇×#732 #11765656

Order 1134.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#732	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	C₃×C₉×D₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×H(3,𝔽₃)	C₂×C₃	1	3	yes	complemented
5	C₃×C₇×C₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×#732	—	7	1	no	maximal, Hall
7	C₃²×D₇	—	3	3	no	—
8	C₃²×D₇	C₃²	1	1	yes	characteristic
9	C₉×D₇	—	3	1	no	—
10	#732	D₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₃²×C₇	—	3	3	no	—
12	C₃²×C₇	C₂×C₃²	1	1	yes	characteristic
13	C₇×C₉	—	3	1	no	—
14	C₂×H(3,𝔽₃)	—	7	3	no	—
15	C₂×C₃×C₉	—	7	1	no	—
16	C₃×D₇	—	3	1	no	—
17	C₃×D₇	—	9	3	no	—
18	C₃×D₇	H(3,𝔽₃)	1	1	yes	characteristic
19	H(3,𝔽₃)	C₃×D₇	1	3	yes	complemented
20	C₃×C₉	C₃×D₇	1	1	yes	characteristic, complemented
21	C₃×C₇	—	3	1	no	—
22	C₃×C₇	—	9	3	no	—
23	C₃×C₇	C₂×H(3,𝔽₃)	1	1	yes	characteristic
24	C₂×C₃²	—	7	1	no	—
25	C₂×C₃²	—	21	3	no	—
26	C₂×C₉	—	21	1	no	—
27	D₇	#732	1	1	yes	characteristic, direct product factor, Hall
28	C₃²	—	3	3	no	—
29	C₃²	C₃²×D₇	1	1	yes	characteristic
30	C₉	—	3	1	no	—
31	C₇	C₂×#732	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	7	1	no	—
33	C₂×C₃	—	21	1	no	—
34	C₂×C₃	—	63	3	no	—
35	C₃	—	3	1	no	—
36	C₃	—	9	3	no	—
37	C₃	D₇×H(3,𝔽₃)	1	1	yes	characteristic
38	C₂	—	7	1	no	Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.